Girl nickname for Connelly

I guess that we have decided to go with Irish surnames for our children. We named our son Sullivan, nn Sully and now named our daughter ConnellyLucille. I am having a little baby name remorse, but I do still really love the name. The problem is that the nn Nelly is a little too close to Sully. What nickname's can you suggest that begin with the letter "C"? I still want her initials to still be CL_. I hope that I didn't miss different Irish surname that would have fit her better.
Thanks!